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Adaptive wavelet backstepping control for a class of mimo underactuated systems

This paper presents an adaptive backstepping controller for a class of multi input multi output (MIMO) underactuated system, with uncertain dynamics, in its original nonsquare form. | Journal of Automation and Control Engineering Vol. 3, No. 4, August 2015 Adaptive Wavelet Backstepping Control for a Class of MIMO Underactuated Systems A. Kulkarni Medicaps Institute of Technology and Management, Indore, India Email: a.kulkarni17@gmail.com A. Kumar School of Electronics, DAVV, Indore, India Email: dr.abhaykumar@gmail.com Abstract—This paper presents an adaptive backstepping controller for a class of multi input multi output (MIMO) underactuated system, with uncertain dynamics, in its original nonsquare form. The proposed controller combines a wavelet based backstepping controller and a robust control term to obtain the desired tracking performance. Proposed scheme utilizes the concept of regularized inverse for effective decoupling of subsystems. Uncertain system dynamics is estimated by using wavelet network. The wavelet parameters are tuned online using Lyapunov approach. The overall control scheme guarantees the ultimate upper boundedness of all closed loop signals. Finally a simulation study is carried out to demonstrate the effectiveness of proposed control scheme. Back stepping design offers a systematic framework to design tracking and regulation control schemes for a wide class of state feedback linearizable nonlinear systems [9]. One of the distinguishable feature of this scheme is to shape performance. The conventional backstepping approach can suitably extended to uncertain nonlinear systems via adaptive backstepping [10]-[12]. Due to their universal approximation property neural networks have been proved as a promising tool for identification and control of dynamical systems. Application of neural network as system identification tool has greatly relaxed the constraint applied on nonlinearities to be linear in parameter thereby broadening the class of the uncertain nonlinear systems which can be effectively dealt by adaptive controllers. Several researchers have combined the conventional feedback control approaches with adaptive .